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A015564 Expansion of x/(1 - 7*x - 6*x^2). 3
0, 1, 7, 55, 427, 3319, 25795, 200479, 1558123, 12109735, 94116883, 731476591, 5685037435, 44184121591, 343399075747, 2668898259775, 20742682272907, 161212165468999, 1252941251920435, 9737861756257039, 75682679805321883 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths: 1, 1, 1, 1, 12, 1, 4, 2, 3, 12, 15, 1, 168, 4, 12, 4, 288, 3, 18, 12, ... - R. J. Mathar, Aug 10 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Lucyna Trojnar-Spelina, Iwona Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.

Index entries for linear recurrences with constant coefficients, signature (7,6).

FORMULA

a(n) = 7*a(n-1) + 6*a(n-2).

a(n) = (1/73)*(7/2 + (1/2)*sqrt(73))^n*sqrt(73) - (1/73)*sqrt(73)*(7/2 - (1/2)*sqrt(73))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008

MATHEMATICA

Join[{a=0, b=1}, Table[c=7*b+6*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)

LinearRecurrence[{7, 6}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 7, -6) for n in xrange(0, 21)] # Zerinvary Lajos, Apr 24 2009

(MAGMA) [n le 2 select n-1 else 7*Self(n-1) + 6*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-7*x-6*x^2))) \\ G. C. Greubel, Dec 30 2017

CROSSREFS

Sequence in context: A198689 A320091 A172743 * A070997 A122372 A083068

Adjacent sequences:  A015561 A015562 A015563 * A015565 A015566 A015567

KEYWORD

nonn,easy,changed

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 15 19:18 EST 2019. Contains 329149 sequences. (Running on oeis4.)